Temperature compensation and temperature … CK2 levels several-fold by gene duplication leads to a decreasing period at higher temperature, whereas decreasing CK2 levels leads to

Temperature compensation and temperature sensationin the circadian clockPhilip B. Kidda,b, Michael W. Younga, and Eric D. Siggiab,1

aLaboratory of Genetics, Rockefeller University, New York, NY 10065; and bCenter for Physics and Biology, Rockefeller University, New York, NY 10065

Edited by Susan S. Golden, University of California, San Diego, La Jolla, CA, and approved October 8, 2015 (received for review June 8, 2015)

All known circadian clocks have an endogenous period that isremarkably insensitive to temperature, a property known as temper-ature compensation, while at the same time being readily entrainedby a diurnal temperature oscillation. Although temperature com-pensation and entrainment are defining features of circadian clocks,their mechanisms remain poorly understood. Most models presumethat multiple steps in the circadian cycle are temperature-depen-dent, thus facilitating temperature entrainment, but then insist thatthe effect of changes around the cycle sums to zero to enforcetemperature compensation. An alternative theory proposes that thecircadian oscillator evolved from an adaptive temperature sensor: agene circuit that responds only to temperature changes. This theoryimplies that temperature changes should linearly rescale the ampli-tudes of clock component oscillations but leave phase relationshipsand shapes unchanged. We show using timeless luciferase reportermeasurements and Western blots against TIMELESS protein that thisprediction is satisfied by the Drosophila circadian clock. We also re-view evidence for pathways that couple temperature to the circadianclock, and show previously unidentified evidence for coupling be-tween the Drosophila clock and the heat-shock pathway.

circadian clock | temperature compensation | mathematical models

Circadian rhythms are daily oscillations in gene expression andprotein concentration that regulate sleep (1, 2), metabolism

(3, 4), and a host of other biological processes (5–8). Circadianoscillations are known to be present in nearly all animals andplants, as well as some fungi and bacteria (9). In all organisms inwhich circadian oscillations have been observed, circadian os-cillations satisfy three defining properties (10). First, circadianoscillations are self-sustained and spontaneously maintain a pe-riod of about 24 h. Second, the circadian rhythm is sensitive tolight and temperature and can be synchronized to external os-cillations in the quantity of either. Third, the period of the cir-cadian oscillation is “temperature-compensated”; that is, theendogenous period of the oscillation is relatively insensitive totemperature.The genetic basis of circadian clocks has been elucidated in

considerable detail over the past two decades, particularly in thefruitfly Drosophila melanogaster, the mouse Mus musculus, and thebread mold Neurospora crassa (11). In Drosophila, a self-sustainedcircadian oscillation in neurons is generated when a pair of proteins,PERIOD (PER) and TIMELESS (TIM), dimerize and, after somedelay, translocate into the nucleus, where the proteins repress theirown transcription by inactivating a transcription factor dimer com-posed of the proteins CLOCK and CYCLE. Light sensitivity ismediated by the blue light photoreceptor CRYPTOCHROME(CRY), which upon activation binds TIMELESS and promotesTIMELESS degradation. A remarkably similar mechanism under-lies circadian clocks in mouse and Neurospora. The circadian clockof cyanobacteria has also been studied in detail but has a signifi-cantly different structure (12, 13).Much is therefore known about the first two defining prop-

erties of circadian clocks. Temperature compensation, however,remains poorly understood despite having been a key problem inchronobiology for nearly the entire history of the field (14, 15).In part, this lack of understanding is because the mechanisms

that set the 24-h circadian period are not fully known. Manytranscriptional regulatory programs are carried out in a matter ofminutes (see, for example, refs. 16 and 17), so generating a 24-hcircadian rhythm requires extensive regulation to generate longtime delays. In wild-type (WT) Drosophila, the translocation ofthe PER-TIM dimer into the nucleus takes about 6–8 h (18, 19)and relies on a complex set of protein interactions and chemicalmodifications. The delay between peak expression of per and timmRNA and protein is also long, about 6 h in constant darkness inWT (see Fig. 2 and Fig. S1), and mRNA stability and processingare also subject to circadian regulation (20). Although manydetails about these processes are known (21), the full set of re-actions setting the associated time scales is not. Additionally, the12- to 14-h length of the combined transcriptional/translationaldelay and nuclear translocation time does not fully account forthe 24-h period of the clock.Not knowing the full set of chemical reactions that contribute

to determining the circadian period has made research into thetemperature compensation difficult. However, some period-determining reactions are known, and experiments on thosereactions have provided some insight, albeit fragmentary, intothe nature of temperature compensation. Nuclear translocationof PER and TIM relies on many complicated chemical modi-fications, in particular, daily rhythms of phosphorylation (22, 23)involving the enzymes casein kinase 2 (CK2) (24, 25), DOUBLE-TIME [a casein kinase 1 (CK1) homolog] (26–28), SHAGGY[a glycogen synthase kinase (GSK-3) homolog] (23), andothers (21). An experiment that altered gene dosages in Neu-rospora has shown that the activity of CK2 has a strong influ-ence on the period of the circadian rhythm (29). Additionally,

Significance

Circadian clocks in animals, plants, and fungi possess the re-markable property of temperature compensation: the clock hasa temperature-insensitive period, while retaining the ability tosynchronize to temperature cycles. The conservation of tem-perature compensation across clades means it is likely criticalto the function of circadian clocks. Temperature compensationalso places the circadian clock in contrast to other biologicalpathways, which generally have temperature-sensitive timescales. However, the mechanism of temperature compensationremains unknown. We present a general scheme by which acircadian oscillator can be temperature-compensated while stillsynchronizing to environmental temperature cycles. In partic-ular, we give experimental evidence that the circadian clockconsists of a temperature-insensitive core oscillator coupled toa specific adaptive temperature signaling pathway.

Author contributions: P.B.K., M.W.Y., and E.D.S. designed research; P.B.K. performed re-search; P.B.K., M.W.Y., and E.D.S. analyzed data; and P.B.K., M.W.Y., and E.D.S. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1511215112/-/DCSupplemental.

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increasing CK2 levels several-fold by gene duplication leads toa decreasing period at higher temperature, whereas decreasing CK2levels leads to an increasing period at higher temperature. Anotherexperiment in mammalian cell culture used a chemical screen toidentify CK1 as a key period-determining enzyme (30). Knockdownof CK1 leads to a loss of temperature compensation, and, most in-terestingly, the phosphorylation rate of CK1 was independentlytemperature-compensated in an in vitro assay. It should be pointedout, however, that the substrate in this assay was an artificial peptide,not a physiologically relevant CK1 target, making the in vivo impli-cations of the experiment unclear. In the flowering plant Arabidopsis,it has been shown that temperature-dependent changes in the con-centration of CK2 and CCA1 are required for temperature com-pensation (31). In Drosophila, the equilibrium level of PER/TIMbinding is temperature-compensated (32). These experiments pro-vide interesting hints into how temperature compensation isachieved at the biochemical level, but no clear picture has emerged.Temperature compensation of the circadian period does not

imply that the circadian clock simply ignores temperature, and itis known that the clock can be entrained by temperature oscil-lations as small as 1° C (33) in Drosophila, and that temperaturehas an important role in regulating circadian physiology (34). Thetraditional solution to this problem has been to posit that theperiod-determining processes of the clock are all temperature-sensitive but that the changes in their rates cancel out to leave theoverall period unaffected by changes in temperature. This processresults in an oscillator that is both temperature-entrainable andtemperature-compensated. This type of procedure underlies nearlyall of the theoretical literature on temperature compensation(see ref. 35 for an early example and ref. 36 for a review); here,we refer to it as the “network model.” There are several prob-lems with the network model approach. First, as Hong et al. (37)have pointed out, many period-affecting mutations in circadiangenes do not affect temperature compensation, which is difficultto explain in a model where careful balancing of rates is requiredto allow temperature compensation. Second, some experimentshave suggested that specific signaling pathways are present formediating circadian temperature sensation (38–44) and that re-moving these pathways eliminates phase shifting of the clock inresponse to temperature changes. These results cast doubt on theidea that the entire circadian clock is temperature-sensitive.Here, we provide experimental support for an entirely different

view of the mechanism of temperature compensation. We showthat the period-determining processes in the core circadian clockare all independently temperature-compensated and that a dedi-cated signaling pathway must therefore be responsible for circadiantemperature sensation. We refer to this scheme as the “pathwaymodel.” This type of model was first suggested by François et al.(45), based on the computational evolution of circadian networkswith the twin properties of temperature entrainment and periodcompensation. The computation built the circadian clock around atemperature-sensing module that was adaptive, responding only totemperature changes, and in that way, encoded the two desiredproperties. The pathway models make two main predictions. First,there should be a specific pathway (or perhaps a few pathways) fortemperature sensation by the circadian clock. Second, the concen-tration of the protein and mRNA components of the clock shouldscale in a simple fashion with temperature. In particular, the overallamplitude or average value of an oscillation in any given componentcan change with temperature, but the shape of the oscillation andthe phase relationships between different oscillating componentsshould remain approximately the same at any temperature (at leastwithin a physiological range).In this respect, the pathway model is consistent with (although

independent of) another model for temperature compensation,the “amplitude model.” In this model, first developed by Lakin-Thomas et al. (46), temperature compensation is achieved by acancelation between an increase in amplitude and an increase in

rate at high temperatures. The relationship between these modelsis examined further in the Discussion.In this paper, we present compelling evidence against the net-

work model and in favor of the pathway model for temperaturecompensation. We first argue for the generality of the scaling andpathway predictions using a simple mathematical model. We thenpresent experimental evidence from quantitative Western blot andluciferase reporter experiments demonstrating that the simplescaling prediction is satisfied by the circadian clock in Drosophila.We provide support for the prediction of specific signaling path-ways by showing that knockouts in the heat-shock pathway affectboth circadian temperature phase shifting and temperature regu-lation of sleep behavior. Finally, we discuss the implications ofthese results and suggest some ideas for continuing work on cir-cadian temperature compensation.

ResultsTemperature Scaling in Some Simple Examples. We begin by devel-oping a simple mathematical example of the pathway model. Themodel features three main components: an mRNA X that istranslated into a protein Y, which has an alternate modification stateZ. Each main component actually consists of a pair of reversiblyinterconverted isoforms, X/X*, Y/Y *, and Z/Z* (diagrammed in Fig.1A). All of the kinetics are linear except the repression of X=X* byZ=Z*. In the simple limit where each isoform is replaced by a singlespecies, the model is equivalent to the Goodwin oscillator model(47) and is described by the following equations:

_X =kXZn − dXX

_Y = kYX − dYY

_Z= kZY − dZZ,

[1]

for some Hill coefficient n, production rates ki, and degradationrates di. Note we have assumed that the Michaelis–Menten kinet-ics in the first term in _X are totally unsaturated, a slight modifi-cation from ref. 47 that does not affect the behavior because Zn islarge. François et al. (45) showed that by a simple rescaling of theunits for X, Y, and Z, one can obtain the modified system

_x=1zn− dXx

_y= x− dY y

_z= y− dZz,

[2]

in which the production coefficients ki have vanished withoutchanging the di and without rescaling time. This result impliesthat a change in any of the ki can be reversed by a rescaling ofconcentration units, leaving the shape of the orbit and its pe-riod unchanged. The Goodwin oscillator can thus be made intoa temperature-compensated/temperature-entrainable oscilla-tor by making the di independent of temperature and at leastone of the ki temperature-sensitive. The effect of changes intemperature will then be described by the simple rescalinggiven above, just as predicted by the evolved models in ref.45. To see how the degradation rates di can be rendered tem-perature-independent in a natural way, we restore the isoformpairs shown in Fig. 1A. This adjustment leads to a pair of equationsfor X=X* :

_X =kX

ðZ+Z*Þn − dX − fXX + rXX*

_X*=kX

ðZ+Z*Þn − d*X*− rXX*+ fXX ,[3]

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where fX and rX represent the forward and reverse rates of con-version between X and X*, respectively (assumed much fasterthan the period-determining circadian rates). Similar equationscan be written for Y=Y * and Z=Z*. Adding the above equationstogether gives back the simplified form in 1, except with X and Zreplaced by sums ðX +X*Þ and ðZ+Z*Þ, and an effective degra-dation rate given by

dX = dK

1+K+ d*

11+K

, [4]

where K = rX=fX is the equilibrium constant describing the balancebetween X and X*. The effective rate dX can be rendered temper-ature-independent by letting d*=K � d and having K increase withtemperature, so that increases in d and d* are cancelled by a shiftin the equilibrium toward the more slowly degraded isoform. Inparticular, we can set d= 0 always and describe the temperaturedependence of rates d* and K = rX=fX by an Arrhenius formexpð−E=kTÞ with energies Ed* and EK =Er −Ef , respectively.The effective rate dX will be temperature-independent as longas K � 1 at room temperature and EK = Ed*.In this case, the model will behave exactly as the temperature-

compensated Goodwin oscillator discussed above and will show a

simple scaling of oscillation shape with temperature. Addition-ally, although the model is abstract, it shares a number of fea-tures with the real circadian clock. In particular, it is knownthat in Drosophila, per and tim mRNA are present in multipleisoforms (48) and that PER and TIM proteins are subject toreversible biochemical modifications that alter the proteins’degradation rates (49, 50). The model serves as a useful para-digmatic example of the pathway model and additionally showsthat independent temperature compensation of all reactions in abiological oscillator can be accomplished without an excessivelycomplicated network. Of course, temperature compensation inthe Goodwin model can be achieved by a constraint imposed onthe di, but in this case, the shape of the orbits will change withtemperature, as is easily seen by simulation.We can extend this example using a simple qualitative argu-

ment, which is depicted in Fig. 1B. Consider a time course ofTIM protein levels over the course of 24 h in constant darkness.TIM protein will be at a minimum at subjective midday and amaximum at subjective midnight. The rising phase of TIM con-centration corresponds to transcription and translation of timmRNA during the late day, the peak phase corresponds to nu-clear translocation of the PER-TIM dimer, and the falling phasecorresponds to repression of TIM production and degradationof the dimer. If all of these subprocesses of the clock havetemperature-dependent rates, such that a shortening of oneprocess is compensated by a lengthening in another, then weshould expect the shape of the curve of TIM protein oscillationto change with temperature. For example, if at higher tem-peratures, a shortening in nuclear translocation time is canceledby a lengthening in transcription/translation times, then weshould expect a narrowing of the portion of the curve whereTIM levels are high (because of more rapid repression of timtranscription) and a corresponding widening of the part of thecurve where TIM levels are low (because of slowing in TIMproduction). This possibility is shown in Fig. 1B.

Western Blot and Luciferase Measurements. To test for the shapeinvariance of the circadian oscillations, we measured the oscil-lations of different components of the circadian clock inD. melanogaster at three different temperatures: 18°C, 25°C, and29° C. We chose to measure the oscillation in TIM protein levels (byWestern blot) and transcription rate (by observing appearance ofa luciferase reporter protein) to get a picture of both the positive(transcriptional) and negative (posttranslational) sides of theclock feedback loop (Fig. 1B). In both cases, WT flies wereprepared by synchronization in at least 3 d of a light-dark (LD) cycleat the requisite temperature, followed by transfer into constantdarkness (DD) at the same temperature. Measurements weremade on the second day in constant darkness to minimize theresidual effects of light while not allowing too much desynch-ronization of the population. For Western blots, yw flies weresampled by flash freezing every hour, and TIM concentrationswere measured relative to cadherin (CDH). Results are shown inFig. 2. For luciferase measurements, groups of 30–50 flies carryinga timeless luciferase (tim-luc) reporter (shown to recapitulatethe dynamics of tim expression reported in ref. 51) were put into a35-mm dish filled with luciferin-containing cornmeal food andobserved in a Hamamatsu top-counting luminescence detector.Results are shown in Fig. 3.Representative blot images are shown in Fig. 2A, from which it

is clear that TIM levels increase at higher temperatures. Fig. 2Bshows samples from two different temperatures (18° C and 29° C)run side-by-side on the same gel. A quantification combining thedata from each of these gels (with three biological replicates) isshown in Fig. 2C. This quantification shows that both the am-plitude and average of TIM oscillations increase with tempera-ture. In Fig. 2D, the curves are shown after a rescaling bysubtracting a linear trend (so that the mean is 0 throughout)

Fig. 1. (A) Diagram of a simple model for oscillator temperature compen-sation. mRNA isoforms X/X* are translated into proteins Y/Y*, which areconverted into a second form Z/Z*, which represses transcription of X/X*.Each half of an isoform pair can be reversibly converted into and plays thesame role as the other but has a different degradation rate. (B) Circadianoscillation of TIM protein, with various phases of the daily circadian cyclemarked on corresponding locations on the oscillation. In red, a hypotheticalscenario is shown in which a change in temperature causes a shortening ofnuclear translocation time and a compensating increase in transcriptiontime, leading to a change in shape of the oscillation.

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and normalizing the root-mean-square (rms) deviation fromthe mean to 1. This process leads to a precise collapse of thecurves onto each other, confirming the simple scaling pre-diction of the model discussed above.In Fig. 3A, representative raw luciferase data at 25° C are

shown. The decaying trend is attributable to depletion of theluciferin substrate (52) but can be easily subtracted. Fig. 3B

shows the same data after detrending by subtracting a 30-hmoving average and smoothing in a 1-h window (time points aretaken every 15 min). Fig. 3C shows the oscillations at the threetemperatures, on the second day in constant darkness, afterrescaling by mean subtraction and normalization of the rms de-viation. Again the curves collapse onto each other, confirmingthe simple scaling prediction. One might object that luciferase

Fig. 2. TIM protein Western blots at three different temperatures. Representative blot images are shown on the left. In A, bands correspond to time points2 h apart as shown, covering a full day at the indicated temperature. B shows bands from the first 6 h of the day at both 18° C and 29° C (as labeled) run side-by-side. C shows quantification of TIM protein concentrations relative to CDH, normalized so that the mean of the 18° C time series is 1. D shows that the samecurves effectively coincide after rescaling to a mean of 0 and an rms deviation of 1. All error bars are SEM for three biological replicates.

Fig. 3. Luminescence from tim-luc flies at 18°C, 25°C, and 29° C. (A) Sample of raw luminescence data plotted in millions of photon cpm. (B) The same dataafter detrending and smoothing. (C) Rescaled luminescence curves from tim-luc flies at different temperatures, taken from the second day in constantdarkness. Shaded areas indicate SEM across three repetitions of the experiment.

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activity and stability are temperature dependent. We performedquantitative PCR (qPCR) measurements of tim mRNA levels attwo different temperatures to show that mRNA oscillations scalesimilarly to luminescence oscillations and that the delay betweenpeak mRNA concentration and luminescence levels is indepen-dent of temperature. Data are shown in Fig. S1, confirming thatluminescence and qPCR data are consistent, with a delay ofabout 4–5 h at both 18° C and 25° C.It is useful in assessing these data to have a control experiment

in which one would expect to see changes in the shape of thecurve of TIM oscillation at different temperatures. Our argu-ments in Temperature Scaling in Some Simple Examples implythat any mutant with a temperature-dependent change in rate forsome circadian process should show a corresponding change inthe shape of its oscillations. The perL mutant has a substantialdefect in temperature compensation [the period increases from27 h at 18°C to 31 h at 29° C (53)]. Fig. 4A shows the results ofWestern blots from perL flies, and Fig. 4B shows luciferasemeasurements from perL; tim-luc flies, after rescaling in bothcases. A shift in the peak of the curves with temperature is evi-dent and has a magnitude significantly larger than what would beexpected from the difference in periods alone. It is worthpointing out that molecular circadian oscillations in perL arenoisier and have lower relative amplitude than in WT (Fig. S2and data in refs. 52 and 54). However, the shift in peaks isstatistically significant.Fig. 4C shows the position of the peaks in protein and lumi-

nescence oscillations for both WT and perL at all three tem-peratures. Peak times are measured relative to the natural periodfor each strain, so for WT flies, 0.5 corresponds to 12 h. Wedgesare centered at the position of the peaks, with widths corre-sponding to the uncertainty in position of the peaks found fromfitting a sine function. From these data, it is clear that in the perLbackground, there is not only a shift in the peaks at differenttemperatures, but the phase difference between luminescenceand protein peaks is also temperature-dependent. This findingconfirms that a change in shape is present, as predicted by ourmodel, and that our method is able to detect such changes re-liably. It is important to keep in mind that (in WT flies) the peakin luminescence lags peak mRNA concentration by about 5 h(Fig. S1), so that the true tim mRNA peak precedes the TIMprotein peak at all temperatures.It is interesting that a yeast two-hybrid experiment (55), as

well as stains of circadian neurons (32), suggests that the defectin perL temperature compensation may be attributable to atemperature-dependent effect on PER-TIM binding, which inturn leads to a delay in nuclear translocation. The increasingdelay in nuclear translocation likely explains the progressivedelay in the peak of protein and mRNA expression and explainsthe narrowing of the gap between protein concentration andtranscription levels, because a defect in repression of timtranscription by PER/TIM protein would allow relatively highlevels of protein and mRNA to be present simultaneously. Theeffect of PER/TIM binding on TIM stability (56) may also playa role in determining how temperature influences the shape ofthe curves in Fig. 4, but in any case it is clear that strongtemperature effects are present in the perL background that areabsent in WT.The other prediction of our model is the presence of a specific

signaling pathway for coupling the circadian oscillation to tem-perature. As briefly mentioned earlier, a significant amount ofevidence for this proposition has already been found. Glaseret al. (41) and Sehadova et al. (43) have found that mutationsassociated with the function of mechanosensitive chordotonalorgans affect circadian temperature entrainment. In particu-lar, morning anticipation in hot–cold cycles is eliminated andluciferase reporter oscillations damp out rapidly under tem-perature entrainment in mutants of the genes nocte and norpA.

Animals lacking functional temperature-sensitive TrpA chan-nels have been shown to entrain more slowly to temperaturecycles and to have noisier molecular rhythms under temperature

A

B

C

Fig. 4. (A) TIM protein oscillations in perL flies, rescaled to have mean0 and rms deviation 1. CT corresponds to a 30-h period with hour 0 beingsubjective morning on the second day in DD. Error bars are SEM for threebiological replicates. (B) Rescaled luminescence curves from perL; tim-lucflies at different temperatures, taken from the second day in con-stant darkness, showing a change in shape. Shaded areas indicateSEM across three different experiments. (C ) Peaks of protein (solid lines)and luminescence (dotted lines) oscillations show a change in rela-tive phase in perL. Each wedge is centered on the peak phase, with thewidth of the wedges giving the error in the location the peak (de-termined by a sinusoidal fit). Wedges on the inner circle come from perL

flies, and wedges on the outer circle come from WT flies. Phase labelsaround the two concentric circles correspond to fractions of the periodfor each strain. The wedges corresponding to WT are offset slightly toaid visibility.

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entrainment (40). One experiment has shown that flies carrying anull mutation in the photoreceptor cryptochrome (cryb) showreduced phase shifts in response to a 30-min 37° C heat shock(42). However, experiments performed in our own laboratory(Fig. S3) have failed to find this effect, and subsequent work byother groups has cast doubt on the role of cryptochrome incircadian temperature entrainment (57, 58). New data from thelaboratory of Patrick Emery (39) suggest that calcium signal-ing is essential for circadian temperature responses and thatthe above-mentioned neural pathways converge by calcium-dependent degradation of TIM.Given that there are clearly multiple pathways present for

communicating temperature to the clock, it may be difficult toeliminate circadian temperature entrainment in an intact mutantanimal. However, virtual elimination of temperature phase-shifting has been achieved in mouse fibroblasts subjected topharmacological inhibition of the heat-shock pathway (38). It hasalso been shown that a knockout of the HSF1 transcription factoraffects circadian expression in fibroblasts under temperature cyclesand that there is a physical association between HSF1 and themammalian circadian transcription factor BMAL1 (44). We weretherefore interested in looking for an effect of the heat-shockpathway on circadian temperature sensation in Drosophila.The Drosophila heat-shock response is mediated by the single

transcription factor HSF. HSF is required for embryonic devel-opment, but viable heterozygous knockouts and a temperature-sensitive mutant (inactive above 30° C) are available (59). Weperformed phase-resetting curve (PRC) experiments on thesemutants, using a temperature step from 18°C to 29° C as thestimulus. The results are shown in Fig. 5A. The phase shifts arecomputed relative to the circadian time (CT) 13 sample, ratherthan a control population. This is because the shape of activityoscillations in WT flies is significantly different at 18°C and 29° C,making a principled phase comparison between temperaturesimpossible. The CT 13 time point was chosen as a reference be-cause at that time point the phase shift relative to a controlappeared small by eye, but the choice is essentially arbitrary. Bothheterozygous and temperature-sensitive heat-shock mutants showincreased phase-shifting in response to temperature steps. This isdifferent from what is seen in mammalian fibroblasts, and thedifference is likely explained by the presence of neural tempera-ture signaling pathways in Drosophila, which presumably interactwith the cell autonomous heat-shock pathway in complex ways.We performed a control experiment by repeating the above

procedure but replacing the stimulus with a temperature stepdown, from 25°C to 18° C. In this case (Fig. S4), the phase shiftsare comparable in WT and heterozygous HSF knockouts, as onemight expect, because the heat-shock pathway should not beactivated at these temperatures. It is interesting to note that theshape of the curves are different in the two experiments, sug-gesting that the mechanisms of circadian temperature sensationare different for warm and cold temperatures. This was alsosuggested by experiments in ref. 60, which found that a specifi-cally cold-sensitive RNA-binding protein influences circadiantranscription in mice, as well as prior work examining circadianresponses to cold temperatures (61, 62).Intriguingly, the heat-shock pathway also appears to have an

effect on the daily distribution of sleep at different temperatures.WT Drosophila tend to sleep more during the day and less atnight at high temperatures (63), as shown in Fig. 5B. However,heterozygous HSF knockouts show a similar distribution of sleepat both 18°C and 29° C (Fig. 5C). This finding suggests that, inDrosophila at least, the heat-shock pathway may also have anunexpected role in regulation of sleep by temperature.

Discussion and ConclusionWe have presented experimental evidence supporting a pathwaymodel for the effects of temperature on the circadian oscillator

based on the theory in reported in ref. 45. By observing twocomponents of the core clock which oscillate with differentphases (TIM protein and tim expression reported by a luciferaseconstruct), we have shown that only the amplitude but not theshape of the circadian oscillation changes with temperature.Parallel experiments in perL mutant flies whose circadian periodvaries from 27 to 31 h over the accessible temperature rangewere an important control. In this case, the oscillations changedshape substantially at different temperatures, demonstrating ourexperiments had sufficient sensitivity.For a typical nonlinear oscillator, whether mechanical or bio-

chemical, it is completely unexpected to observe oscillations at

A

B

C

Fig. 5. (A) Results of a PRC experiment applying a temperature step from18° C to 29° C to three strains of flies. HSF/- indicates a heterozygous knockout ofthe heat-shock transcription factor, and HSFTS indicates a temperature-sensitiveHSF mutant. Phase shifts are plotted against the hour of the subjective day atwhich the step occurred and are calculated relative to the phase of the group atCT 13. Error bars are SEM. (B and C) Effect of temperature on sleep profile in WTand heat-shock mutant flies. Sleep per 30 min is shown over the course of thecircadian day at 18° C and 29° C in WT flies (B) and heterozygous heat-shocktranscription factor knockouts (C). Shaded regions indicate SEM across at least 15individuals.

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different parameter values that can be superimposed by shiftingmeans and linearly scaling amplitudes. In ref. 45, this propertyemerged by in silico evolution that favored temperature en-trainment and period compensation. The computation beganfrom an initial gene network that responded adaptively tochanges in temperature. That is, the computation registeredchanges in temperature but returned to the same operating pointirrespective of temperature in the absence of change. Adaptationis a common property of sensory systems. Computational evolu-tion then built a delayed negative-feedback oscillator around theadaptive temperature sensor and with it the properties selectedfor, namely temperature compensation and temperature entrain-ment. There is certainly parameter tuning in this model as there isin the network model, which is perfectly reasonable because nat-ural evolution has plausibly shaped the phenotype of the circadianoscillator. However, there was no direct computational selectionfor the linear rescaling of orbits between different temperatures,and that property has to be considered as an emergent conse-quence of the basic assumptions of entrainment and period com-pensation. In the simple example we proposed, the scaling of orbitsresults from the specific form of the model equations, and it wouldbe interesting to understand more abstractly why the same propertyarose from the evolutionary computation. In general, our resultsindicate that the linear superposition of orbits at different tem-peratures is a generic property of circadian oscillators.It is much less clear how to experimentally test the starting

assumption reported in ref. 45: that an adaptive temperaturesensor is the dominant coupling responsible for temperatureentrainment. The suppression of the heat-shock pathway wasshown to eliminate temperature phase shifting in mouse fibro-blasts (38, 44). However, an organism may be much more com-plicated in this regard than single cells. We demonstrated acoupling between the heat-shock pathway and the circadianclock in Drosophila but found that heat-shock pathway mutantsdisplay increased sensitivity to temperature. This suggests thatother pathways are present for temperature signaling in Dro-sophila. We also showed that heat-shock mutants lack the normaltemperature dependence of daily sleep distribution, suggesting arole for the heat-shock pathway in sleep regulation.It is important to note that we do not suggest that temperature

signaling via the heat-shock pathway is a universal mechanism ofcircadian clocks. Indeed, our own data (Fig. S4) suggest thatseparate mechanisms are present for hot and cold responseseven with Drosophila. New data from the laboratory of PatrickEmery (39) suggest that the various neural pathways involved incircadian temperature signaling all act via calcium-dependentdegradation of TIM through the SOL protease pathway. Thedata show that inhibiting calcium signaling significantly reducescircadian phase shifts in response to temperature changes and,most interestingly, that the calcium response to a temperaturestep appears to be adaptive, just as our model predicts.Our claim that each period-influencing process in the circa-

dian clock is independently temperature-compensated raises thequestion of how such compensation could be achieved. Wepresented a mathematical model showing how the pathway modelscheme can be implemented in a variant of the Goodwin model. Inour model, temperature entrainment was achieved by allowing theproduction rates of proteins or mRNA to be temperature-dependent, because these rates affect the quantity of oscillatingcomponents but not the period. Although the model does not insiston coupling temperature to the clock via transcription rates, themodel is consistent with evidence that transcriptional signaling viathe heat-shock pathway is responsible for temperature phaseshifting in mammalian fibroblasts (38, 44). It has also been shownthat the period of the circadian clock is buffered against changes intranscription rates in both mammalian cells (64) and Drosophila(65), which is also consistent with the assumptions of our model.Additionally, our model implements temperature compensation by

balancing changing degradation rates against a shifting betweenpaired isoforms for each mRNA and protein in the model. Suchinterconvertible isoforms with varying degradation rates are knownto be present in the circadian clock, both in mRNA (48) andproteins (49, 50).It is also worth noting that the mathematical model predicts

that the increase in transcription/translation rates with temper-ature leads to a change in the amplitude of oscillation. Thismodel has the expected feature that when the production rate ofthe ith variable increases, the corresponding amplitude of oscil-lation increases as well. In that sense it, is consistent with thepredictions of the amplitude model for temperature compensa-tion proposed in ref. 46. This model proposes that an increase inrates at higher temperature can be canceled by a proportionalincrease in amplitude, without specifying precisely how thecompensation occurs. The amplitude model is supported by dataon zebrafish circadian transcription (66), as well as by Drosophilaphase-resetting curve experiments, both recent (67) and canon-ical (62). Evidence for increase in amplitude at higher temper-atures has also been found in Neurospora (68) and cyanobacteria(69). Interestingly, this increase in circadian amplitude withtemperature may also provide a mechanism for seasonal adap-tation of the clock in Drosophila (70). Our own data (Fig. 2C)show that the amplitude of TIM oscillations roughly doublesbetween 18° and 29° C, which is consistent with the typical de-pendence of biological reaction rates on temperature (71). In-sofar as the amplitude model remains agnostic about exactly howcompensation is achieved, the model can be regarded as compli-mentary to, and in some sense independent of, the pathway model.In sum, our data, combined with model of François et al. (45),provide the first experimental support to our knowledge for a the-ory of the complete temperature compensation of a temperature-entrainable oscillator.Our results have broad implications for future research into

the mechanisms of temperature compensation. We have shownthat temperature compensation is not a network-wide processbut that each period-setting process of the clock must betemperature-compensated on its own. Experimental results ontemperature compensation must be interpreted in this context.Future work is needed to understand the temperature compen-sation of nuclear translocation, transcriptional repression, andnuclear export and degradation, among other processes. Nucleartranslocation is a particularly promising avenue for future re-search. A great deal about the biochemistry of nuclear trans-location has been discovered in the last decade (19), and much ofthis knowledge can be leveraged into experiments on tempera-ture compensation. Additionally, the multifarious network ofreversible phosphorylations known to regulate nuclear trans-location of the PER-TIM dimer bears an intriguing resemblanceto models of temperature compensation in the literature (72,73). Another promising avenue for research is single-cell timelapse observations. Work in Drosophila S2 cells has contributedsignificantly to the understanding of PER-TIM dynamics (cf. ref.19). The advent of fluorescent protein-tagging experiments onthe circadian clock in Neurospora (74, 75), as well as reporterexperiments in mammalian fibroblasts (76), will allow observa-tion of the effect of temperature changes on multiple subpro-cesses of the circadian clock in a single experiment. Elucidatingthe biochemical mechanisms of temperature compensation inthe circadian clock remains an open problem.

MethodsStrains. Western blots were performed on Drosophila strains yw and perL.Luciferase experiments used tim-luc flies obtained from Ralf Stanewsky,University College London, London (51), and perL; tim-luc flies generated bycrossing tim-luc to a perL;IF/CyO;sb/TM6 balancer line. Temperature PRCexperiments used iso31 and strains hsf1 and hsf4 (59), obtained from theBloomington Stock Center.

E6290 | www.pnas.org/cgi/doi/10.1073/pnas.1511215112 Kidd et al.

Western Blots and qPCR. Flies were entrained for at least 3 d in a 12 h:12 h LDcycle at a given temperature, then moved into constant darkness at the sametemperature. Measurements began at CT 0 on the second day in DD (36 hafter the last lights off). Flies were flash frozen on dry ice every hour for 24 h(or 30 for perL), and heads were isolated for protein or RNA extraction.

For protein, heads were homogenized in an equal volume of radio-immunoprecipitation (RIPA) buffer (50 mM Tris, pH 8; 150 mM NaCl; 1 mMEDTA; 1% Triton-X 100 by volume; 0.5% sodium deoxycholate; 20% glycerolby volume; 0.02% NaN3), supplemented with 1 mM DTT and protease in-hibitor mixture (Calbiochem). Homogenate was mixed with a double volumeof dilution buffer (RIPA buffer without Triton-X, sodium deoxycholate, DTT,and protease inhibitor), and centrifuged twice for 10 min at 4° C. Extractswere quantitated and resolved by SDS/PAGE. Blots were probed with ratanti-TIM (77) at 1:1,000 and rat anti-CDH (Santa Cruz Biotechnology) at1:200. HRP-conjugated secondary antibodies (Jackson ImmunoResearch)were applied at 1:10,000 and imaged with ECL 2 (enhanced chemiluminescence)substrate (Thermo Scientific) on a Bio-Rad ChemiDoc.

For RNA, extracts were homogenized with TRIzol (Invitrogen) and thencolumn-purified with an RNeasy Mini Kit (Qiagen) according to the manu-facturer’s protocol, including DNase treatment (Qiagen). RNA solutions werequantitated and then reverse-transcribed with iScript reverse transcriptase(Bio-Rad). QCPRs on the resulting cDNA were performed with PerfeCTa SYBRGreen FastMix (Quanta Biosciences) in a LightCycler 480 (Roche) and ana-lyzed by the ΔΔ Ct method. The primers for tim were taken from ref. 78, andthe primers for the housekeeping gene gapdh were from ref. 79.

Luciferase Measurements. Flies were entrained in the manner describedabove, and during the day on the last day of entrainment, about 50 maleflies were placed in a 30-mm plate containing about 1–2 mL of standardcornmeal/molasses fly food supplemented with 15 mM D-luciferin (potassiumsalt; Biosynth) layered on top of 7 mL of standard food. At the time of lights

out (zeitgeber time 12), the plates were placed in the wells of a LM-2400photon detection unit (Hamamatsu) for measurement. The resulting rawdata were detrended by subtracting a 30-h moving average and smoothedby averaging time points in a 1-h window.

Behavior Measurements. For temperature step phase-shifting experiments,flies in a Drosophila activity monitor (Trikinetics) were entrained for at least3 d in a 12 h:12 h LD cycle at 18° C and then moved into DD at 18° C. On thesecond day in DD, monitors were moved at the indicated time to a differentincubator at 29° C. Behavior was measured for at least 5 d subsequently, andphase shifts were determined by computing a cross-correlation functionbetween activity traces. For heat-shock phase-shifting experiments, WT andcryb flies [the laboratory of Michael Rosbash, Brandeis University, Waltham,MA (80)] were entrained similarly and then placed in constant darkness in acustom-built small incubator designed to provide rapid and precise temper-ature stimuli from a Peltier effect heating/cooling element (Custom Ther-moelectric). Temperature was increased from 25° C to 37° C for 30 min at CT15 on the first day in DD. Phase shifts were computed as before, by com-paring to a control group kept at 25° C.

Sleep measurements were made in DD using flies entrained in the samemanner and judging sleep asbeginning after a 5-min period of inactivity (81, 82).

ACKNOWLEDGMENTS. We thank Paul François, Stuart Brody, and membersof M.W.Y.’s laboratory for helpful discussions. We thank Ralf Stanewsky andMichael Rosbash for providing strains and Ralf Stanewsky for helpful advicerelated to luciferase measurements. We thank Patrick Emery for providing uswith a manuscript of his in-press paper on calcium signaling. This researchwas funded by National Science Foundation Grants PHY-0954398 and PHY-1502151 (to E.D.S.) and National Institutes of Health Grant GM054339(to M.W.Y.).

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